2023/06/30 by David Reinhardt, Reinhardt, David B., Dean Lee +5
Physics and Astronomy · #Advanced Fiber Laser Technologies #Cold Atom Physics and Bose-Einstein Condensates #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nuclear Theory (nucl-th) #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2306.17720
openalex publication_date 2023/06/30 · openalex created_date 2023/07/04 · openalex updated_date 2026/07/28
The nonlinear Schrödinger equation (NLSE) is a rich and versatile model, which in one spatial dimension has stationary solutions similar to those of the linear Schrödinger equation as well as more exotic solutions such as solitary waves and quantum droplets. Here we present the unified theory of the NLSE, showing that all stationary solutions of the local one-dimensional cubic-quintic NLSE can be classified according to a single number called the cross-ratio. Any two solutions with the same cross-ratio can be converted into one another using a conformal transformation, and the same also holds true for traveling wave solutions. Further, we introduce an optimization afterburner that relies on this conformal symmetry to substantially improve NLSE parameter estimation from noisy empirical data. The new method therefore should have far reaching practical applications for nonlinear physical systems.